Married filing separately. I filed standard and my wife filed itemized. Do I have to do something to correct it or should I just wait until IRS tells me what to do next?

[TomK]

If you are married filing separately (MFS), you must both file using the standard deduction or the itemized deduction.  One of you will need to change your deduction method.  If your return doesn't get rejected by the IRS first, someone will have to amend his/her return.

Please read this TurboTax FAQ about amending your 2018 tax return: How to amend (change or correct) a return you already filed.

[Opus 17]

The IRS will eventually send a letter to the taxpayer who used the standard deduction that they must itemize.  They may include a bill for tax assuming zero itemized deductions.  If that’s what you would have done anyway, you can pay the bill instead of filing an amended return.  Or, you can file an amended return to claim whatever itemized deductions you have.  You can also amend now, without waiting.  

If you wait until after April 15 to amend, on your own or waiting for the IRS notice, you will also pay interest and late payment penalties of about 1% per month of the amount of tax you owe.